{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T13:21:16Z","timestamp":1719926476289},"reference-count":30,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2016,3,1]],"date-time":"2016-03-01T00:00:00Z","timestamp":1456790400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T00:00:00Z","timestamp":1583107200000},"content-version":"vor","delay-in-days":1462,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Symbolic Computation"],"published-print":{"date-parts":[[2016,3]]},"DOI":"10.1016\/j.jsc.2015.03.005","type":"journal-article","created":{"date-parts":[[2015,3,23]],"date-time":"2015-03-23T08:58:46Z","timestamp":1427101126000},"page":"87-103","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":2,"special_numbering":"C","title":["Geometry of the ringed surfaces in R<\/mml:mi><\/mml:mrow>4<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:math> that generate spatial Pythagorean hodographs"],"prefix":"10.1016","volume":"73","author":[{"given":"Rida T.","family":"Farouki","sequence":"first","affiliation":[]},{"given":"Robert","family":"Gutierrez","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.jsc.2015.03.005_br0010","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1080\/00029890.1975.11993807","article-title":"There is more than one way to frame a curve","volume":"82","author":"Bishop","year":"1975","journal-title":"Am. Math. Mon."},{"key":"10.1016\/j.jsc.2015.03.005_br0020","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1016\/S0167-8396(02)00165-6","article-title":"Euler\u2013Rodrigues frames on spatial Pythagorean-hodograph curves","volume":"19","author":"Choi","year":"2002","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.jsc.2015.03.005_br0030","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1015294029079","article-title":"Clifford algebra, spin representation, and rational parameterization of curves and surfaces","volume":"17","author":"Choi","year":"2002","journal-title":"Adv. Comput. Math."},{"key":"10.1016\/j.jsc.2015.03.005_br0040","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0167-8396(93)90037-4","article-title":"An algebraic approach to curves and surface on the sphere and on other quadrics","volume":"10","author":"Dietz","year":"1993","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.jsc.2015.03.005_br0050","series-title":"Homographies, Quaternions, and Rotations","author":"Du Val","year":"1964"},{"key":"10.1016\/j.jsc.2015.03.005_br0060","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/0167-8396(94)90204-6","article-title":"The conformal map z\u2192z2 of the hodograph plane","volume":"11","author":"Farouki","year":"1994","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.jsc.2015.03.005_br0070","series-title":"Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable","author":"Farouki","year":"2008"},{"key":"10.1016\/j.jsc.2015.03.005_br0080","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10444-009-9138-3","article-title":"Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves","volume":"33","author":"Farouki","year":"2010","journal-title":"Adv. Comput. Math."},{"key":"10.1016\/j.jsc.2015.03.005_br0090","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/S0167-8396(02)00123-1","article-title":"Structural invariance of spatial Pythagorean hodographs","volume":"19","author":"Farouki","year":"2002","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.jsc.2015.03.005_br0100","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1023\/A:1016280811626","article-title":"Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves","volume":"17","author":"Farouki","year":"2002","journal-title":"Adv. Comput. Math."},{"key":"10.1016\/j.jsc.2015.03.005_br0110","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.cagd.2007.09.007","article-title":"Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures","volume":"25","author":"Farouki","year":"2008","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.jsc.2015.03.005_br0120","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1090\/S0025-5718-2011-02519-6","article-title":"Design of rational rotation-minimizing rigid body motions by Hermite interpolation","volume":"81","author":"Farouki","year":"2012","journal-title":"Math. Comput."},{"key":"10.1016\/j.jsc.2015.03.005_br0130","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1016\/j.cagd.2013.03.001","article-title":"Rotation-minimizing Euler\u2013Rodrigues rigid-body motion interpolants","volume":"30","author":"Farouki","year":"2013","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.jsc.2015.03.005_br0150","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.cagd.2007.01.004","article-title":"Rational space curves are not \u201cunit speed\u201d","volume":"24","author":"Farouki","year":"2007","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.jsc.2015.03.005_br0140","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1016\/j.jsc.2010.03.004","article-title":"Rational rotation-minimizing frames on polynomial space curves of arbitrary degree","volume":"45","author":"Farouki","year":"2010","journal-title":"J. Symb. Comput."},{"key":"10.1016\/j.jsc.2015.03.005_br0160","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.jsc.2011.09.012","article-title":"A complete classification of quintic space curves with rational rotation-minimizing frames","volume":"47","author":"Farouki","year":"2012","journal-title":"J. Symb. Comput."},{"key":"10.1016\/j.jsc.2015.03.005_br0170","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0167-8396(89)90008-3","article-title":"Computing frames along a trajectory","volume":"6","author":"Guggenheimer","year":"1989","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.jsc.2015.03.005_br0180","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/j.cagd.2007.09.006","article-title":"Nonexistence of rational rotation-minimizing frames on cubic curves","volume":"25","author":"Han","year":"2008","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.jsc.2015.03.005_br0190","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1016\/S0167-8396(01)00065-6","article-title":"Gn-continuous connections between normal ringed surfaces","volume":"18","author":"Hartmann","year":"2001","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.jsc.2015.03.005_br0210","series-title":"Geometry and the Imagination","author":"Hilbert","year":"1952"},{"key":"10.1016\/j.jsc.2015.03.005_br0200","series-title":"The Fourth Dimension","author":"Hinton","year":"1904"},{"issue":"1","key":"10.1016\/j.jsc.2015.03.005_br0220","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1007\/BF01457962","article-title":"\u00dcber die Abbildungen der dreidimensionalen Sph\u00e4re auf die Kugelfl\u00e4che","volume":"104","author":"Hopf","year":"1931","journal-title":"Math. Ann."},{"key":"10.1016\/j.jsc.2015.03.005_br0230","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0167-8396(93)90049-9","article-title":"A new intersection algorithm for cyclides and swept surfaces using circle decomposition","volume":"10","author":"Johnstone","year":"1993","journal-title":"Comput. Aided Geom. Des."},{"key":"10.1016\/j.jsc.2015.03.005_br0240","series-title":"Advances in Robot Kinematics: Analysis and Control","first-page":"413","article-title":"Rotation minimizing spherical motions","author":"J\u00fcttler","year":"1998"},{"key":"10.1016\/j.jsc.2015.03.005_br0250","series-title":"Geometric Modeling: Algorithms and New Trends","first-page":"1","article-title":"The rational B\u00e9zier representation for conics","author":"Lee","year":"1987"},{"key":"10.1016\/j.jsc.2015.03.005_br0260","series-title":"Geometry of Four Dimensions","author":"Manning","year":"1914"},{"key":"10.1016\/j.jsc.2015.03.005_br0270","series-title":"Elementary Geometry","author":"Roe","year":"1993"},{"key":"10.1016\/j.jsc.2015.03.005_br0280","doi-asserted-by":"crossref","first-page":"4375","DOI":"10.1016\/j.cam.2012.04.002","article-title":"Pythagorean-hodograph curves in Euclidean spaces of dimension greater than 3","volume":"236","author":"Sakkalis","year":"2012","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.jsc.2015.03.005_br0290","series-title":"Lectures on Classical Differential Geometry","author":"Struik","year":"1961"},{"key":"10.1016\/j.jsc.2015.03.005_br0300","series-title":"Riemannian Geometry and the Tensor Calculus","author":"Weatherburn","year":"1950"}],"container-title":["Journal of Symbolic Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717115000309?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717115000309?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T08:49:03Z","timestamp":1583138943000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0747717115000309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3]]},"references-count":30,"alternative-id":["S0747717115000309"],"URL":"https:\/\/doi.org\/10.1016\/j.jsc.2015.03.005","relation":{},"ISSN":["0747-7171"],"issn-type":[{"value":"0747-7171","type":"print"}],"subject":[],"published":{"date-parts":[[2016,3]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Geometry of the ringed surfaces in that generate spatial Pythagorean hodographs","name":"articletitle","label":"Article Title"},{"value":"Journal of Symbolic Computation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jsc.2015.03.005","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2015 Elsevier Ltd. All rights reserved.","name":"copyright","label":"Copyright"}]}}